Details

analyze289.0ms (7.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample45.0ms (1.1%)

Algorithm

1×

intervals

Results

13.0ms	16×	body	512	valid
8.0ms	188×	body	128	valid
6.0ms	34×	body	1024	valid
5.0ms	256×	pre	128	true
1.0ms	15×	body	256	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify227.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

1179×	`div-sub_binary64`
672×	`sub-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
422×	`associate-/l*_binary64`
385×	`distribute-rgt-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	39	19
3	63	19
4	104	19
5	204	19
6	320	19
7	513	19
8	943	19
9	2087	19
10	2930	19
11	3705	19
12	3906	19
13	4077	19
14	4165	19
15	4198	19
16	4200	19
17	4320	19
18	4594	19
19	4698	19
20	4698	19
21	5018	19

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

16.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.2b	(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)

Compiler

Compiled 45 to 33 computations (26.7% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
2.4b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite82.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

15.5b

Rules

58×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
19×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 65

Calls

2 calls:

15.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
10.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 1149 to 611 computations (46.8% saved)

series82.0ms (2.1%)

Error

0.0b

Counts

2 → 30

Calls

2 calls:

32.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
28.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 1827 to 1414 computations (22.6% saved)

simplify104.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

447×	`distribute-rgt-in_binary64`
395×	`distribute-lft-in_binary64`
345×	`times-frac_binary64`
319×	`associate-/l*_binary64`
226×	`cancel-sign-sub-inv_binary64`

Counts

95 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	2391
1	516	2356
2	1549	2248
3	4660	2248
4	5032	2248

prune57.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	3	85

Error

Counts

85 → 3

Alt Table

Status	Error	Program
	16.2b	(/.f64 (+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1) 2)
▶	15.8b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (+.f64 -1 (/.f64 alpha (+.f64 alpha (+.f64 2 beta))))) 2)
	45.7b	(/.f64 (/.f64 (+.f64 2 (*.f64 2 beta)) alpha) 2)

Compiler

Compiled 1639 to 1061 computations (35.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 alpha (+.f64 alpha (+.f64 2 beta)))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (+.f64 -1 (/.f64 alpha (+.f64 alpha (+.f64 2 beta)))))
2.4b	(+.f64 -1 (/.f64 alpha (+.f64 alpha (+.f64 2 beta))))

rewrite132.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

74×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
30×	`add-sqr-sqrt_binary64`
27×	`distribute-lft-out_binary64`
25×	`add-cube-cbrt_binary64`

Counts

4 → 109

Calls

4 calls:

22.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (+.f64 -1 (/.f64 alpha (+.f64 alpha (+.f64 2 beta)))))
11.0ms	(+.f64 -1 (/.f64 alpha (+.f64 alpha (+.f64 2 beta))))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
6.0ms	(/.f64 alpha (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 2702 to 1733 computations (35.9% saved)

series145.0ms (3.6%)

Error

Counts

4 → 54

Calls

4 calls:

37.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (+.f64 -1 (/.f64 alpha (+.f64 alpha (+.f64 2 beta)))))
29.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
24.0ms	(/.f64 alpha (+.f64 alpha (+.f64 2 beta)))
19.0ms	(+.f64 -1 (/.f64 alpha (+.f64 alpha (+.f64 2 beta))))

Compiler

Compiled 3247 to 2413 computations (25.7% saved)

simplify172.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

679×	`times-frac_binary64`
551×	`associate-/l*_binary64`
328×	`cancel-sign-sub-inv_binary64`
236×	`sub-neg_binary64`
168×	`distribute-rgt-in_binary64`

Counts

163 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	3505
1	718	3440
2	2319	3343
3	4974	3343
4	4958	3343

prune87.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	138	3	141

Error

Counts

141 → 3

Alt Table

Status	Error	Program
▶	16.2b	(/.f64 (+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1) 2)
✓	15.8b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (+.f64 -1 (/.f64 alpha (+.f64 alpha (+.f64 2 beta))))) 2)
	45.7b	(/.f64 (/.f64 (+.f64 2 (*.f64 2 beta)) alpha) 2)

Compiler

Compiled 3029 to 2022 computations (33.2% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))
0.1b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha)))
2.4b	(+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1)

rewrite235.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

276×	`*-un-lft-identity_binary64`
218×	`times-frac_binary64`
143×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
80×	`distribute-lft-out_binary64`

Counts

3 → 212

Calls

3 calls:

35.0ms	(+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1)
14.0ms	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha)))
10.0ms	(/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))

Compiler

Compiled 3996 to 2546 computations (36.3% saved)

series106.0ms (2.7%)

Error

Counts

3 → 42

Calls

3 calls:

32.0ms	(+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1)
30.0ms	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha)))
21.0ms	(/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))

Compiler

Compiled 2425 to 1916 computations (21% saved)

simplify279.0ms (7%)

Algorithm

1×	egg-herbie

Rules

553×	`distribute-rgt-in_binary64`
474×	`distribute-lft-in_binary64`
462×	`times-frac_binary64`
277×	`cancel-sign-sub-inv_binary64`
208×	`sub-neg_binary64`

Counts

254 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	6432
1	643	6007
2	2089	5771
3	4962	5771
4	4974	5771

prune90.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	231	3	234

Error

Counts

234 → 3

Alt Table

Status	Error	Program
✓	16.2b	(/.f64 (+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1) 2)
✓	15.8b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (+.f64 -1 (/.f64 alpha (+.f64 alpha (+.f64 2 beta))))) 2)
▶	45.7b	(/.f64 (/.f64 (+.f64 2 (*.f64 2 beta)) alpha) 2)

Compiler

Compiled 2767 to 1746 computations (36.9% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (+.f64 2 (*.f64 2 beta)) alpha)

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

5.0ms

(/.f64 (+.f64 2 (*.f64 2 beta)) alpha)

Compiler

Compiled 518 to 398 computations (23.2% saved)

series20.0ms (0.5%)

Error

Counts

1 → 9

Calls

1 calls:

18.0ms

(/.f64 (+.f64 2 (*.f64 2 beta)) alpha)

Compiler

Compiled 217 to 173 computations (20.3% saved)

simplify87.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

578×	`distribute-rgt-out_binary64`
472×	`times-frac_binary64`
457×	`div-sub_binary64`
353×	`associate-l_binary64`
347×	`associate-/l*_binary64`

Counts

38 → 19

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	69	639
1	158	592
2	364	592
3	874	592
4	3161	571
5	4426	571
6	5341	571

prune10.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	19	0	19
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	19	3	22

Error

Counts

22 → 3

Alt Table

Status	Error	Program
	16.2b	(/.f64 (+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1) 2)
	15.8b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (+.f64 -1 (/.f64 alpha (+.f64 alpha (+.f64 2 beta))))) 2)
	45.7b	(/.f64 (/.f64 (+.f64 2 (*.f64 2 beta)) alpha) 2)

Compiler

Compiled 235 to 188 computations (20% saved)

regimes530.0ms (13.3%)

Accuracy

Total 0.2b remaining (50.1%)

Threshold costs 0.2b (50.1%)

Compiler

Compiled 9040 to 6407 computations (29.1% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	53
1	34	53
2	37	53
3	39	53
4	40	53
5	39	53

end3.0ms (0.1%)

Compiler: Compiled 38 to 27 computations (28.9% saved)

sample1.1s (28.4%)

Algorithm

1×

intervals

Results

274.0ms	5949×	body	128	valid
183.0ms	8000×	pre	128	true
178.0ms	1040×	body	1024	valid
77.0ms	585×	body	512	valid
27.0ms	320×	body	256	valid
24.0ms	106×	body	2048	valid

Compiler

Compiled 111 to 82 computations (26.1% saved)

Details

analyze289.0ms (7.3%)

sample45.0ms (1.1%)

simplify227.0ms (5.7%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite82.0ms (2.1%)

series82.0ms (2.1%)

simplify104.0ms (2.6%)

prune57.0ms (1.4%)

localize13.0ms (0.3%)

rewrite132.0ms (3.3%)

series145.0ms (3.6%)

simplify172.0ms (4.3%)

prune87.0ms (2.2%)

localize11.0ms (0.3%)

rewrite235.0ms (5.9%)

series106.0ms (2.7%)

simplify279.0ms (7%)

prune90.0ms (2.3%)

localize6.0ms (0.1%)

rewrite21.0ms (0.5%)

series20.0ms (0.5%)

simplify87.0ms (2.2%)

prune10.0ms (0.3%)

regimes530.0ms (13.3%)

bsearch3.0ms (0.1%)

simplify5.0ms (0.1%)

end3.0ms (0.1%)

sample1.1s (28.4%)

Profiling